The ideal class groups of hyperelliptic curves(HECs) can be used in cryptosystems based on the discrete loga-rithm problem. Recent developments of computational technolo-gies for scalar multiplications of divisor classes have shown thatthe performance of hyperelliptic curve cryptosystems (HECC) iscompatible to that of elliptic curve cryptosystems (ECC). Espe-cially, genu...

The primes or prime polynomials (over finite fields) are supposed to be distributed ‘irregularly’, despite nice asymptotic or average behavior. We provide some conjectures/guesses/hypotheses with ‘evidence’ of surprising symmetries in prime distribution. At least when the characteristic is 2, we provide conjectural rationality and characterization of vanishing for families of interesting infini...

In this paper, we describe an improvement of the Berlekamp algorithm for binomials xn−a over prime fields Fp. We implement the proposed method for various cases and compare the results with the original Berlekamp method. The proposed method can be extended easily to the case where the base field is not a prime field.

We present a heuristic asymptotic formula as x → ∞ for the number of isogeny classes of pairing-friendly elliptic curves over prime fields with fixed embedding degree k ≥ 3, with fixed discriminant, with rho-value bounded by a fixed ρ0 such that 1 < ρ0 < 2, and with prime subgroup order at most x.

A new Gaussian dispersion model, the Plume Rise Model Enhancements (PRIME), has been developed for plume rise and building downwash. PRIME considers the position of the stack relative to the building, streamline deflection near the building, and vertical wind speed shear and velocity deficit effects on plume rise. Within the wake created by a sharp-edged, rectangular building, PRIME explicitly ...